The Pennsylvania State University Schreyer Honors College

THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE

DEPARTMENTS OF ENGINEERING SCIENCE AND MECHANICS AND ELECTRICAL ENGINEERING

EVALUATION ON COUPLING STRATEGIES FOR ULTRA-HIGH FIELD MRI PROBE MADE OF CYLINDRICAL DIELECTRIC RESONATOR

RUI LIU

SPRING 2016

A thesis submitted in partial fulfillment of the requirements for a baccalaureate degrees in Electrical Engineering and Engineering Science with interdisciplinary honors in Electrical Engineering and Engineering Science

Reviewed and approved* by the following:

Michael T. Lanagan Professor of Engineering Science and Mechanics Thesis Supervisor and Honors Adviser

Jeffrey Mayer Associate Professor of Electrical Engineering Honors Adviser

Steven E. Perini Technical Staff of Material Research Institution Faculty Reader

* Signatures are on file in the Schreyer Honors College and Engineering Science and Mechanics Office. i

ABSTRACT

Research into the properties of ceramic dielectric resonators (CDR) showed potential applications in magnetic resonance imaging (MRI). Replacing traditional radiofrequency (RF) coils in current design with ceramic dielectric resonators would improve signal-to-noise ratio

(SNR) and spectral resolution that render an enhanced imaging quality. The objective of this research project is to investigate alternative coupling methods and probe designs to achieve ideal resonance frequency and power transmission for optimized performance. Specifically, Network

Analyzer was utilized for investigating different coupling configurations targeting 14 Tesla pre- clinical MRI machines. Several coupling methods were investigated: a full loop around the resonator (previous work), a double loop around the resonator, a triple loop around the resonator and a quadruple loop around the resonator. The result showed that by implementing a triple loop around the resonator, the effective power transmission was increased by 157% to -10.656 dB compared to previous design. Further, with modified copper tuning pieces, the resonant frequency could be tuned down to the operating frequency of 600 MHz, which solved the previous problem of a minimum resonant frequency of 605 MHz. The current triple loop prototype design turned out to be the best coupling configuration with relative high power transmission, low SNR and a tunable frequency range covering 600 MHz.

TABLE OF CONTENTS

LIST OF FIGURES ...... iii

ACKNOWLEDGEMENTS ...... v

Chapter 1 LITERATURE REVIEW ...... 1

1.1 History ...... 1 1.2 Theory ...... 3 1.2.1 Theory of Operation ...... 4 1.2.2 Mode Designation and Mode Chart ...... 5 1.2.3 Characterization ...... 7 1.3 Applications in MRI Fields ...... 8

Chapter 2 MATERIALS AND METHODS ...... 11

2.1 Resonator Characterization and Probe Setup ...... 11 2.2 Coupling Methods ...... 13 2.3 Electromagnetic Simulations ...... 14

Chapter 3 RESULTS...... 17

3.1 Single Loop Side Coupled ...... 17 3.2 Single Loop Center Coupled ...... 18 3.3 Single Loop Edge Coupled ...... 19 3.4 Double Loop ...... 20 3.5 Triple Loop ...... 22 3.6 Quadruple Loop ...... 23 3.7 Final Design Characterization ...... 24

Chapter 4 DISCUSSION AND CONCLUSION ...... 25

BIBLIOGRAPHY ...... 28

iii

LIST OF FIGURES

Figure 1. (a) Dielectric resonators, (b) Magnetic-wall waveguide below cutoff model of a dielectric resonator...... 3

Figure 2. Modes in a dielectric resonator (~800 MHz).1 ...... 5

Figure 3. Mode chart for a dielectric post resonator.9 ...... 6

Figure 4. (a) Hakki-Coleman method,12 (b) typical laboratory setup utilizing a Network Analyzer.8

Figure 5. Coupling strategy proposed by Haines.13 (a) simulation schematic, (b) probe head assembly, (c) circuit schematic ...... 10

Figure 6. Coupling strategy proposed by Pyrz.17 ...... 10

Figure 7. (a) Probe prototype assembly, (b) 3D model of the assembly ...... 12

Figure 8. Five coupling methods with six setups ...... 13

Figure 9. (a) 3D model for setup 1 (single loop aside), (b) back view, (c) top view ...... 15

Figure 10. (a) 3D model for setup 2 (full loop around), (b) back view, (c) top view ...... 15

Figure 11. (a) 3D model for setup 3 (full loop edge coupled), (b) back view, (c) top view ..... 15

Figure 12. (a) 3D model for setup 4 (double loop), (b) back view, (c) top view ...... 16

Figure 13. (a) 3D model for setup 5 (triple loop), (b) back view, (c) top view ...... 16

Figure 14. (a) 3D model for setup 6 (quadruple loop), (b) back view, (c) top view ...... 16

Figure 15. Setup 1 (a) experimental setup, (b) B field distribution, (c) E field distribution .... 17

Figure 16. Simulated S11 response of setup 1 ...... 18

Figure 17. Setup 2 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution 19

Figure 18. Simulated S11 response of setup 2 ...... 19

Figure 19. Setup 3 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution 20

Figure 20. Simulated S11 response of setup 3 ...... 20

Figure 21. Setup 4 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution 21

Figure 22. Simulated S11 response of setup 4 ...... 21

Figure 23. Setup 5 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution 22 iv

Figure 24. Simulated S11 response of setup 5 ...... 22

Figure 25. Setup 6 (a) no shield, (b) shielded, (c) suspected TE01δ mode B field distribution . 23

Figure 26. Simulated S11 response of setup 6 ...... 23

Figure 27. Full probe head structure with the triple loop configuration ...... 24

Figure 28. S21 parameter: loss at REF value comparison of the six setups ...... 25

Figure 29. Q value comparison of the six setups ...... 26

Figure 30. Resonant frequency comparison of the six setups ...... 27

ACKNOWLEDGEMENTS

I would like to express my deep gratitude to Professor Michael Lanagan, my research supervisor, Steven Perini, my research staff mentor, and Wei Luo, my research PhD mentor, for their patient guidance, enthusiastic encouragement and useful critiques of this research work. I would also like to thank Dr. Thomas Neuberger of Huck Institute of Penn State for his advice and assistance in MRI laboratory. My grateful thanks are also extended to Amanda Baker of the

Material Research Institute for her help in using the CO2 laser-cutter machine. My deepest gratitude towards all their support in my thesis project.

I would also like to extend my thanks to the Haines and Pyrz for their previous researches building foundations for this the coupling problem.

Finally, I wish to thank my parents for their support and encouragement throughout my study. 1

Chapter 1

LITERATURE REVIEW

Dielectric resonators are microwave resonating elements in microwave circuits and systems, such as filters and oscillators. Microwave dielectric resonators are structures of high dielectric constant (εr) and high quality factor (Q), which is the primary limitation of performances of such circuits and systems. Traditional solutions with waveguide structure sacrifice size, weight and cost to compensate for improved Q value. The dielectric resonators, on the other hand, function as waveguide filters and oscillators with the advantage of being small, stable and lightweight.

Significant miniaturization in microwave components can be achieved with the popularization of dielectric resonators, leading towards cost efficient, high performance wireless applications and technologies. With the advent of new high-Q materials, commercial applications of dielectric resonators will be extended to higher frequencies and more engineering fields.1,2 This literature review section briefly presents the history of dielectric resonators, basic theory of operation and technique of characterization, and their recent recognition as resonant elements in Magnetic

Resonance Imaging (MRI) fields.

1.1 History

Great interest and substantial efforts have been given to guided electromagnetic wave propagation in dielectric media even in the early days of microwaves. Researches into long cylinder of dielectric material showed its potential as electromagnetic waveguide. Dielectric 2 resonator’s first appearance in 1939 when its term was introduced by Richtmyer3 of Stanford

University showed that unmetalized dielectric toroid could function as microwave resonator.

However, it was not until 1960s that Okaya and Barash4, researchers from Columbia University, rediscovered dielectric resonators and provided the first modes analysis. In their work on high dielectric materials – single-crystal TiO2 rutile shows high Q resonance in the microwave range.

Okaya and Barash’s work showed potential application of dielectric materials as a practical alternative for metal cavities, which had long been used as microwave resonators.

In the mid-1960s, the first extensive theoretical and experimental evaluation of the dielectric resonator was performed by Cohn5 and his fellows of Rantec Corporation. High-purity

TiO2 ceramic with an isotropic dielectric constant of 100 was experimented. Low loss tangent about 0.0001 and high Q value about 10000 were reported. The band-pass filters constructed from such dielectric resonators reported similar functionality of a waveguide filter 20 to 30 times larger in volume. Nevertheless, in spite of the high Q value and shrunk size, high-dielectric constant materials such as TiO2 rutile exhibited temperature sensitivity about 25 times that of metal wall cavity, resulting correspondingly large resonant frequency instability1.

In the early 1970s, Raytheon6 developed barium tetratitanate ceramic K-38 with a temperature-stable dielectric constant of 38 and an unloaded Q of 2500. This first temperature- stable, low-loss, high-Q material was a real breakthrough for dielectrics in microwave resonator application. A modified barium tetratitanate with superior Q and temperature stability was reported by Bell Labs7. Promising results of dielectric resonators for practical implementation were shaded due to the scarce supply of the compound, which was not ready commercially available. The next breakthrough was brought by Murata Manufacturing Company from Japan8. They developed (Zr–

Sn)TiO ceramics featuring adjustable temperature coefficient and reasonable price. Soon such 3 material became commercially available and dielectric resonator attracted widespread attention.

The significant miniature of size combined with its superior performances boost researches into theoretical work and practical implementation. The development of dielectric resonators as high- quality resonating elements expanded rapidly ever since, serving as band-pass filters, probes, oscillators, and even spreads into Magnetic Resonance Imaging (MRI) territories.

1.2 Theory

A dielectric resonator is a miniature microwave resonator made of material of high dielectric constant and usually comes in the form of a cylindrical disc as shown in Figure 1 (a).

The internal reflections of electromagnetic waves at the high dielectric constant material/air boundary confine the energy within and near the structure, and therefore such dielectric element can function as a microwave resonator. Compared to traditional metal-wall waveguide cavity resonators, dielectric resonators are small, lightweight, low-cost, and stable with low-loss and high-Q. Replacing traditional waveguide structure using dielectric resonators in size-demanding systems such as microwave integrated circuit (MIC) and monolithic microwave integrated circuit

(MMIC) are becoming increasingly popular.1 a b

Figure 1. (a) Dielectric resonators, (b) Magnetic-wall waveguide below cutoff model of a dielectric resonator. 4

1.2.1 Theory of Operation

Theory of operating such dielectric elements has been developed from the conventional magnetic wall concept. The magnetic wall concept states that the normal component of the electric field and the tangential component of a magnetic field vanish at the boundary on such wall. A hypothetical magnetic wall cavity approximation is first constructed to explain the operation of dielectric resonators. In the approximation, the high-dielectric material/air boundary are modeled as a magnetic wall or open circuit. Resonant frequency and electromagnetic field distributions can thereby be calculated analytically.1

Taking the leakage of electromagnetic field from the resonator to its vicinity into consideration, the magnetic wall model is modified and improved by removing lateral magnetic walls and introducing the magnetic wall waveguide below cutoff model shown in Figure 1 (b).

The calculation accuracy of frequency operating at TE01δ mode is about 6%. A mode subscript δ is introduced to describe the leaking field portion.1

Next, the magnetic wall waveguide is also removed rendering an improved accuracy of resonant frequency to about 1-2%. The housing, shielding and other structures, which prevent radiation, in an actual resonator configuration, along with additional factors such as dielectric supports, tuning plate in more advanced models can also be taken into consideration. Then by using the mode matching method, the resonant frequency and the electromagnetic field distribution can be obtained with a high accuracy better than 1%.1

For more complex structures, such that with housing, tuning and coupling elements, 3-D electromagnetic simulation programs can be utilized to provide accurate modeling and visualization of the field distribution and power dissipation. 5

1.2.2 Mode Designation and Mode Chart

Kobayashi proposed the by far most promising mode designation that could be regarded as a standard. Figure 2 presents some of the existing mode designations.1

Figure 2. Modes in a dielectric resonator (~800 MHz).1 6

TE01δ mode in cylindrical resonator and TE11δ mode in rectangular resonator are the most commonly used modes in dielectric resonators. The TE01δ is classified as the fundamental mode because usually it has the lowest resonant frequency corresponding to certain diameter-to-length

(D/L) ratio. However, compared to metal cavity resonator, the nomenclature in a dielectric resonator, in general, is not as well defined. A mode chart is a chart that shows the correspondence of resonant frequency with the D/L ratio. Different material with different dielectric constants will generate different mode charts. These mode charts are very useful as design tools for separating targeted mode from spurious modes/interferences.1,2,9,10 Figure 3 is an example of such mode chart.

Figure 3. Mode chart for a dielectric post resonator.9 7

The TE01δ mode is utilized in single-mode filters and oscillators. The hybrid mode HE11δ is usually used in dual-mode filters, directional filters and oscillators. The TM mode is used in low-frequency filters and cavity combiners.1

Another advantage of such dielectric resonators is the convenience of coupling to common transmission lines. The coupling can be adjusted conveniently by simple displacement of the resonator. Moreover, placing metal components such as screws or plates, allows adjusting the resonant frequency (or tuning) by interfering the magnetic field distribution with a typical range in the order of 10%. In addition, the ease of dielectric shaping is another advantage over the traditional metal wall cavities. Modified shapes of dielectric resonator discs containing notches, flats, holes, housings etc. allows further tuning or other treatments.1

1.2.3 Characterization

The classical dispersion theory states that the dielectric constant is constant at microwave frequencies, and the dielectric loss increases with frequency. Therefore, the basic properties of a certain dielectric material can be described by the product of Q value and frequency. One classical method is the Hakki-Coleman method.1,2,11

The Hakki-Coleman method is the technique of measuring the dielectric and magnetic properties of a homogenous isotropic medium in the range of 3 to 100 kmc. The accuracy of determining the permittivity or permeability of the targeted dielectric material can reach ±0.1%.

The setup is shown in Figure 4 (a) where a cylindrical dielectric resonator rod is placed between two parallel conducting plates. Two or more resonant TE mode frequencies are measured for permittivity and two or more resonant TM mode frequencies are measured for permeability. With 8 the knowledge of the resonant frequencies, resonator dimensions and the unloaded Q value, the permittivity and permeability can thereby be calculated with high precision. The measurement accuracy of the loss tangent, however, is limited by the uncertainty of the surface resistance of the conducting plates. Kobayashi12 improved the Hakki-Coleman method by introducing a technique of measuring the effective surface resistance of the conducting plates and taking the temperature dependence of surface resistance into consideration. Therefore, high precision of small loss tangent measurement can be achieved. Figure 4 (b) demonstrate a typical laboratory setup of performing the Hakki-Coleman method utilizing a Network Analyzer.

1.3 Applications in MRI Fields

Dielectric resonators, coupled with high Q factors and miniature size, has already been widely used as an alternative approach in various microwave systems, including probing devices, miniature antennas, filters, and oscillators1. Research into cylindrical dielectric resonator (CDR) in MRI applications showed promising potentials using CDR to replace traditional radio frequency

(RF) coils in high field strength applications. a b

Figure 4. (a) Hakki-Coleman method,12 (b) typical laboratory setup utilizing a Network Analyzer. 9

Magnetic resonance imaging (MRI) utilizes strong magnetic fields and radio wave to form images of the subject. The technology is widely used in medical imaging to investigate anatomy and function of the body for medical diagnosis. Common clinical MRI scanners operate at a field strength at 1.5 Tesla. Advantages implementing high-field MRI designs (7T to 20T) over current clinical scanners (1.5T to 3T) include increased signal to-noise ratio (SNR), increased resolution and reduced scan time. However, this increase in magnetic field strength demands improvement on the current RF coil resonator design due to increased radiation losses, wavelength effects, self- resonance, and the high resistance at high field application.13 Research into the properties of ceramic dielectric resonators showed potential applications in high-field MRI, typically 7T and

14T. High permittivity and high Q factor ceramic dielectric resonators as an alternative for the traditional RF coil can create strong uniform magnetic fields in a compact structure and potentially solve some of the challenges of high field resonator design.13

Various coupling mechanisms were utilized for TE01δ and HEM11δ such as placing loops at

14,15 the side of the resonator at half-height to detect HEM11 modes ; a single loop at the bottom edge

16 of the resonator for TE01δ mode ; a single loop aside of the resonator at half-height for TE01δ

13 16 mode and eight-channel transmit/receive array of TE01δ mode etc. The results from current researches show promising improvements in scan resolutions and reduction of scanning time. And by finding the optimum coupling configuration, which maximizes the power transmission while maintains the high Q factor at the specified operation frequency for the MRI machine, dielectric resonators will very likely replace the traditional RF coil and rendering popularization of high field strength MRI.

Previous works have reported improvements on coupling strategies with CDRs in TE01δ mode targeting the 14 Tesla MRI machine.13,17 Haines13 proposed a single copper wire loop 10 situated at the side of the CDR at half height (Figure 5). Pyrz17 improved this coupling strategy with a full loop configuration round the CDR at half height (Figure 6). Pyrz reported that the later strategy improved the signal power by 70.6% (compared with reconstructed coupling setup) and

75.7% when integrated in the MRI probe.17 However; the result can only achieve a minimum 605

MHz instead of a resonant frequency of 600 MHz, the 14 T MRI operation frequency. This project will carry out further study on various coupling strategies to maximize signal power, maintaining a relative high Q-value as well as enabling tuning ability to achieve 600 MHz resonance.

Figure 5. Coupling strategy proposed by Haines.13 (a) simulation schematic, (b) probe head assembly, (c) circuit schematic

Figure 6. Coupling strategy proposed by Pyrz.17 11

Chapter 2

MATERIALS AND METHODS

Calcium titanate (CaTiO3) was chosen as the material for the cylindrical dielectric resonator (CDR) due to its wide availability, low price and ease of machining. TE01δ mode was the focus of this project in order to compare with previous coupling strategies. Previous coupling methods resonating at TE01δ mode including a copper ring at the side of the CDR13 and a full loop around the CDR17 were investigated and compared in terms of S21 parameters and Q value. The S21 parameters were used experimentally because they give information on resonant frequency, correspondence with the B1 field strength as well as the calculated unloaded Q value. The center frequency of the S21 peak identifies the resonant mode frequency where the resonator produces the strongest signal intensity. The loss at reference value measures the energy coupling capability in terms of decibels (dB) values. The unloaded Q value was calculated by dividing the center frequency by the 3 dB bandwidth. It describes the loss of the CDR-probe configuration with the higher the Q value, the lower the energy loss. The characterizations of the CDR and coupling strategies were conducted in the laboratory setting utilizing the Anritsu 37369D Lightning Network Analyzer and

CST (Computer Simulation Technology, Darmstadt, Germany) Microwave Studio software package.

2.1 Resonator Characterization and Probe Setup

The CDR investigated in this project was fabricated in advance with following dimensions for the

14 Tesla MRI machine: outer diameter: 46.1 mm, height: 33.7 mm and inner bore diameter: 5.32 mm. The dimensions were designed so that the TE01δ mode resonant frequency of the CDR when coupled falls in a range close to the 600 MHz operation frequency of the 14 Tesla MRI machine. The CDR was characterized using the classic Hakki-Coleman method conducted on the Network Analyzer with S21 parameters. The 12 calculated relative permittivity of the CDR is 173 (εr = 156 for CaTiO3), and the calculated average Q value is 2225.

The coupling strategies of the fabricated resonator were compared in a laboratory setup similar to but slightly different from the Hakki-Coleman method setup. The next section will describe the coupling strategies and laboratory setup in detail. The best coupling method was selected and integrated into the MRI probe prototype.

Once the best strategy was selected, the CDR with coupling copper wire was stationed within acrylic holders mounted on a cylindrical probe body. The acrylic holders were redesigned on

SOLIDWORKS and cutted out from a laser-cutter to fit the dimensions of the CDR. The probe body was constructed from aluminum tubing, brass screw bar skeleton and brass supporting pieces. A plastic tubing was also reserved for water-cooling if needed. Figure 7 shows a photograph of the probe body assembly with the acrylic holders and the SOLIDWORKS models of each component. A copper shield (diameter

54.0 mm) was positioned outside of the probe head around the CDR to complete the full probe setup.

Figure 7. (a) Probe prototype assembly, (b) 3D model of the assembly 13

Tuning of the resonators was achieved by asymmetrically positioning two small pieces of copper foil on each face of the CDR. The two pieces of copper foil were attached to two acrylic pieces stationed on two plastic rods extending from the bottom of the probe body to the top. By adjusting the position of the acrylic tuning pieces using the plastic rod from the bottom, a precise resonant frequency of 600 MHz could be achieved in real time MRI imaging. The impedance matching of the CDR was performed with a variable capacitor in series with the coupling copper wire near the probe head. A control rod was positioned in the center of the probe body extending from the capacitor to the bottom of the probe body. By turning the control rod from the bottom of the probe, one can achieve real time 50 Ω matching in MRI imaging instrument.

2.2 Coupling Methods

Five coupling methods (totally 6 setups) were evaluated in this study: (I) a single loop aside of the resonator at half-height (reconstruction of Haines’ work), (II) a full loop around the resonator

(reconstruction of Pyrz’s work), (III) a double loop around the resonator, (IV) a triple loop around the resonator, and (V) a quadruple loop around the resonator (Figure 8).

Figure 8. Five coupling methods with six setups 14

The coupling strategies of the CDR were investigated using an alternative free space approach rather than the classic Hakki-Coleman setup. Instead of placing the CDR in between two conductive plates, the CDR was rested on top of a non-conductive foam platform with a suspending probe placed inside the central bore at half-height of the cylindrical body. The S21 parameters of the TE01δ mode were measured using the Anritsu 37369D Lightning Network Analyzer. The evaluations of these coupling methods were conducted both with and without the copper shield (with a hole on the wall allowing the suspending probe go through). The best strategy in terms of S21 parameters and Q value was selected and integrated into the probe head prototype. The full integration of the best coupling strategy was again characterized using the method described above before taken to MRI imaging test.

2.3 Electromagnetic Simulations

The electromagnetic responses of the five coupling strategies (totally 6 setups) were simulated using CST Microwave Studio software package. The 3D layouts of the simulation models are shown in

Figure 9 to 14. All the coupling setups simulated laboratory setup with no copper shield and used one port to detect the S11 signal due to the fact that the MRI probe can only supply a S11 value. The models used

Eigen mode solver with a background material of air and open boundary conditions. Ten resonant modes were calculated for each setup and by checking the electric and magnetic field distributions with the mode designation chart, TE01δ mode for each setup was selected and compared.

The resonator was modeled with a relative permittivity of 156 (CaTiO3), outer diameter of 46.1 mm, inner bore diameter of 5.32 mm and height of 33.7 mm. The copper wire loops were model in

SOLIDWORKS and imported to the CST Microwave Studio. The wires were modeled as copper from the built-in material library. The ports were discrete ports with 50 Ω impedance and of type S parameters. Field monitors were set based on the calculated TE01δ modes of each setup.

Figure 9. (a) 3D model for setup 1 (single loop aside), (b) back view, (c) top view

Figure 10. (a) 3D model for setup 2 (full loop around), (b) back view, (c) top view

Figure 11. (a) 3D model for setup 3 (full loop edge coupled), (b) back view, (c) top view

Figure 12. (a) 3D model for setup 4 (double loop), (b) back view, (c) top view

Figure 13. (a) 3D model for setup 5 (triple loop), (b) back view, (c) top view

Figure 14. (a) 3D model for setup 6 (quadruple loop), (b) back view, (c) top view

Chapter 3

RESULTS

This section presents the experimental and simulation results of the proposed coupling strategies.

The results are compared in terms of S21 parameters, Q value as well as resonant frequency. The CST simulations compare the S11 resonant frequencies with the experimental data and look at the insights of the electric and magnetic field distributions within the resonator. Even though the simulation gave only S11 plot, we can still qualitatively infer the information on loss and Q value based on how deep were the dips and how sharp were those dip valleys. The best coupling strategy selected and performed characterization within a complete MRI setup within the probe prototype is also presented in this section to exhibit final design of the project.

3.1 Single Loop Side Coupled

The coupling strategy proposed by Haines13 was reconstructed and simulated in a laboratory setup shown in Figure 15. This coupling setup reported a TE01δ mode resonant frequency of 498.5 MHz, a loss at

REF value of -22.6 dB and a Q value of 434.6. Figure 16 shows the CST simulation of its S11 response. The simulation result agreed with the experimental measurement with a resonant frequency of 493.2 MHz. The

S11 plot showed a relatively sharp dip valley at 493.2 MHz with a response about -0.7 dB.

Figure 15. Setup 1 (a) experimental setup, (b) B field distribution, (c) E field distribution 18

Figure 16. Simulated S11 response of setup 1

3.2 Single Loop Center Coupled

The coupling strategy proposed by Pyrz17 was reconstructed and simulated in a laboratory setup shown in Figure 17. This coupling setup without copper shield reported a TE01δ mode resonant frequency of 549.0 MHz, a loss at REF value of -19.8 dB and a Q value of 39.9. The shielded measurement reported a TE01δ mode resonant frequency of 586.9 MHz, a loss at REF value of -16.6 dB and a Q value of 60.8. The experimental results agreed with Pyrz’ work where a degradation in Q value was sacrificed for an improved effective power transmission.

Figure 18 shows the CST simulation of the S11 response corresponding to the unshielded setup. The simulation result agreed with the experimental measurement with a resonant frequency of 538.8 MHz. The

S11 plot showed a dip valley at 538.8 MHz with a response about -1.5 dB, meaning improved power transmission compared to the one proposed by Haines. The dip valley on the S11 plot was not near as sharp as setup 1, showing a degradation in Q value corresponding to the experimental measurement. The resonant frequency was lower than the 605 MHz proposed by Pyrz because the CDR in this project was fabricated with larger dimensions to decrease the TE01δ mode resonance frequency.

Figure 17. Setup 2 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution

Figure 18. Simulated S11 response of setup 2

3.3 Single Loop Edge Coupled

While investigating the coupling strategy proposed by Pyrz, full loop coupled at the edge of the

CDR reported significant response. Figure 19 shows its experimental setup and field simulation results.

This coupling setup without copper shield reported a TE01δ mode resonant frequency of 516.0 MHz, a loss at REF value of -16.9 dB and a Q value of 102.6. The shielded measurement reported a TE01δ mode resonant frequency of 567.8 MHz, a loss at REF value of -13.7 dB and a Q value of 120.2. The experimental results showed promising improvements on Pyrz’s proposed strategy with both improved Q value and effective power transmission. 20

Figure 20 shows the CST simulation of the S11 response corresponding to the unshielded setup. The simulation agreed with experimental data with a TE01δ mode resonant frequency of 510.4 MHz. The S11 plot showed a sharper dip valley at 510.4 MHz with an improved response to about -4.2 dB compared to the S11 response of Pyrz’s setup at 538.8 MHz. The simulation results agreed with the experimental results showing improvements on both Q value and power transmission.

Figure 19. Setup 3 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution

Figure 20. Simulated S11 response of setup 3

3.4 Double Loop

Inspired by the edge response of the CDR, a double loop configuration was designed. Figure 21 shows the experimental setup and field simulation results. This coupling setup without copper shield reported a TE01δ mode resonant frequency of 555.5 MHz, a loss at REF value of -15.2 dB and a Q value of 21

96.8. The shielded measurement reported a TE01δ mode resonant frequency of 586.5 MHz, a loss at REF value of -11.9 dB and a Q value of 209.5. The experimental results showed improvements on power transmission both with and without copper shielding. The Q value showed degradation without copper shielding compared to the full loop edge coupled setup. With shielding however, the Q value demonstrated a surprisingly increase which was hypothetically caused by better confinement of energy due to the copper shield.

Figure 22 shows the CST simulation of the S11 response corresponding to the unshielded double loop setup. The simulation agreed with experimental data with a TE01δ mode resonant frequency of 553.2

MHz. The dip valley at 553.2 MHz had an improved response about -6.0 dB compared to the edge coupled single loop setup. The sharpness of the valley was visually indistinguishable compared to the full loop edge coupled setup, agreeing to the experimental measurements.

Figure 21. Setup 4 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution

Figure 22. Simulated S11 response of setup 4 22

3.5 Triple Loop

Further developed from double loop idea was the triple loop configuration. Figure 23 shows the experimental setup and field simulation results. This coupling setup without copper shield reported a TE01δ mode resonant frequency of 595.3 MHz, a loss at REF value of -11.6 dB and a Q value of 226.9. The shielded measurement reported a TE01δ mode resonant frequency of 614.3 MHz, a loss at REF value of -

9.2 dB and a Q value of 716.2. The experimental results showed significant improvements on both power transmission and especially Q value with and without copper shielding.

Figure 24 shows the CST simulation of the S11 response corresponding to the unshielded triple loop setup with a TE01δ mode resonant frequency of 572.4 MHz slightly lower than the experimental measurement. The dip valley at 572.4 MHz only had a S11 response of -1.5 dB and were not as sharp as previous configurations suggesting a degradation in power transmission and Q value. The simulation results of the triple loop configuration did not predict the excellent performance because the loops were placed in vicinity of the edges and center of the CDR in experimental setup.

Figure 23. Setup 5 (a) no shield, (b) shielded, (c) B field distribution, (d) E field distribution

Figure 24. Simulated S11 response of setup 5 23

3.6 Quadruple Loop

The quadruple loop configuration is shown in Figure 25. The experimental setup without copper shield reported a TE01δ mode resonant frequency of 627.9 MHz, a loss at REF value of -10.5 dB and a Q value of 266.3. The shielded measurement reported a TE01δ mode resonant frequency of 598.4 MHz, a loss at REF value of -9.9 dB and a Q value of 393.2. The experimental results showed diminishing returns in both power transmission and Q value.

Figure 26 shows the CST simulation of the S11 response corresponding to the unshielded quadruple loop setup. The simulation showed complex field distributions and it was hard to distinguish which mode was the TE01δ mode. The closest magnetic field distribution is shown in Figure 25 (c). The resonant frequency of this suspected mode was 773.6 MHz.

Figure 25. Setup 6 (a) no shield, (b) shielded, (c) suspected TE01δ mode B field distribution

Figure 26. Simulated S11 response of setup 6 24

3.7 Final Design Characterization

Comparing all six coupling strategies in terms of S21 parameter, Q value and resonant frequency, the triple loop configuration was recognized as the optimum coupling strategy for the CDR targeting the

14 T MRI machine. The triple loop configuration had excellent effective power transmission performances while maintaining a relatively high Q value. The TE01δ mode resonant frequency in this configuration was also the closest to 600 MHz. The triple loop configuration also triumphed in its rigid structure and stability in recurring measurement.

The triple loop configuration was integrated into the probe head and characterized. The triple loop copper wire was fixed between acrylic holders held together by nylon screws. Tuning pieces were attached at both sides of the resonator to achieve fine-tuning. The tuning pieces and matching capacitor were controlled via separate plastic rods at the bottom of the probe body. Figure 27 shows the photograph of the complete probe head structure under working condition. When tuned at 600.0 MHz resonance, the probe head reported a loss at REF value of -10.6 dB and a Q value of 346.0. The tuning ability of the probe head was 600 ±5 MHz.

Figure 27. Full probe head structure with the triple loop configuration 25

Chapter 4

DISCUSSION AND CONCLUSION

The comparisons of the six coupling setups in terms of S21 response, Q-values and resonant frequency are presented in Figure 28 to 30. By replacing a single loop coupled on the side of the resonator with coupling loops around the resonator, an increase in the S21 value could be achieved with a sacrifice in

Q value, meaning a gain in B1 field strength with a trade-off in SNR. As the number of the turns of the coupling loop increased, the S21 value increased from -16.6 dB to -9.2 dB and reached diminishing return with four turns; the Q value also increased from 60.8 to 716.2 and started to decrease beyond three turns.

The final designed implemented the triple loop configuration and showed a 157% increase in the effective power transmission compared to previous design proposed by Pyrz.

Figure 28. S21 parameter: loss at REF value comparison of the six setups 26

The measured Q values are related to other contributions in the resonant system described in the following equation:

1 1 1 1 1 = + + + 푄 푄푐 푄푑 푄푟푎푑 푄푒푥

where Qc, Qd, Qrad, and Qex, are the Q-factors that are due to losses in conductor, dielectric resonator, radiation, and external circuitry. The experimental measurement showed that Qex decreases when the external coupling increases, implying a trade-off between S21 parameters and Qex. The equation also implies the overall quality factor is dominated by the smallest Q-factor among the four. Therefore considering lossy samples being imaged in MRI machine, the small Q-factor of the sample rather than the improved Q on coupling and resonator will dominate the overall Q-factor. Therefore, the improvement on S21 parameter or better power transmission is more significant than improvements on Q-value.

Figure 29. Q value comparison of the six setups 27

The simulation showed some insights on field distributions under various coupling strategies. As the looping scheme became more complicated, the fields were no longer uniformly distributed and H fields showed components that are not perpendicular to B0 field. This was troubling since it would render a decrease in the B1 field component that is perpendicular to B0 field. Also the simulation showed the more turns presented, the more distortion was rendered on the field distribution. The distortion could render deviant resonance from TE01δ mode resonance just like the simulation result of the quadruple loop configuration. Although experimentally triple loop configuration was the optimum solution for this CDR targeting the 14 T MRI machine, a simpler coupling strategy would be more desirable to yield uniform B1 field distribution.

Figure 30. Resonant frequency comparison of the six setups

BIBLIOGRAPHY

1. Fiedziuszko, S., & Holme, S. (n.d.). Dielectric resonators raise your high-Q. Microwave

Magazine, IEEE, 2(3), 50-60.

2. Fiedziuszko, S., Hunter, I., Itoh, T., Kobayashi, Y., Nishikawa, T., Stitzer, S., & Wakino, K.

(n.d.). Dielectric materials, devices, and circuits. IEEE Transactions on Microwave Theory

and Techniques, 50(3), 706-720.

3. Richtmyer, R. (n.d.). Dielectric resonator. Journal of Applied Physics, 10, 391-398.

4. Okaya, A., & Barash, L. (n.d.). The Dielectric Microwave Resonator. Proceedings of the IRE,

50, 2081-2092.

5. Cohn, S. (n.d.). Microwave Bandpass Filters Containing High-Q Dielectric Resonators. IEEE

Transactions on Microwave Theory and Techniques, 16, 218-227.

6. Masse, D., Pucel, R., Readey, D., Maguire, E., & Hartwig, C. (n.d.). A new low-loss high-k

temperature-compensated dielectric for microwave applications. Proceedings of the IEEE,

59, 1628-1629.

7. Plourde, J., Linn, D., O'Bryan Jr., H., & Thompson Jr., J. (n.d.). Ba2Ti9O20 as a microwave

dielectric resonator. Journal of the American Ceramic Society, 58, 418-420.

8. Kobayashi, Y., & Senju, T. (n.d.). Resonant modes in shielded uniaxial-anisotropic dielectric

rod resonators. IEEE Transactions on Microwave Theory and Techniques, 41(12), 2198-

2205.

9. Courtney, W. (n.d.). Analysis and Evaluation of a Method of Measuring the Complex

Permittivity and Permeability Microwave Insulators. IEEE Transactions on Microwave

Theory and Techniques, MTT-18, 476-485. 29

10. Rebsch, D., Webb, D., Moore, R., & Cowlishaw, J. (n.d.). A Mode Chart for Accurate Design

of Cylindrical Dielectric Resonators 21 (Correspondence). IEEE Transactions on

Microwave Theory and Techniques, 468-469.

11. Hakki, B., & Coleman, P. (n.d.). A Dielectric Resonator Method of Measuring Inductive

Capacities in the Millimeter Range. IEEE Transactions on Microwave Theory and

Techniques, MTT-8, 402-410.

12. Kobayashi, Y., & Katoh, M. (n.d.). Microwave Measurement of Dielectric Properties of Low-

Loss Materials by the Dielectric Rod Resonator Method. IEEE Transactions on Microwave

Theory and Techniques, MTT-33, 586-592.

13. Haines, K., Neuberger, T., Lanagan, M., Semouchkina, E., & Webb, A. (n.d.). High Q calcium

titanate cylindrical dielectric resonators for magnetic resonance microimaging. Journal of

Magnetic Resonance, 200(2), 349-353.

14. Aussenhofer, S., & Webb, A. (n.d.). High-permittivity solid ceramic resonators for high-field

human MRI. NMR in Biomedicine, 26(11), 1555-1561.

15. Aussenhofer, S., & Webb, A. (n.d.). Design and evaluation of a detunable water-based

quadrature HEM11 mode dielectric resonator as a new type of volume coil for high field

MRI. Magnetic Resonance in Medicine, 68(4), 1325-1331.

16. Aussenhofer, S., & Webb, A. (n.d.). An eight-channel transmit/receive array of TE01 mode

high permittivity ceramic resonators for human imaging at 7T. Journal of Magnetic

Resonance, 243, 122-129.

17. Pyrz, M., Lanagan, M., Perini, S., Neuberger, T., Chen, F., & Semouchkina, E. (2013)

Optimization of Electromagnetic Coupling to Ceramic Resonators for Magnetic Resonance

Imaging Applications. CICMT, 2013, 000069-000075. 30